1. Solving Absolute Value Inequalities
Algebra 2 Unit 1, Lesson 2.3

2. Solving Absolute Value Inequalities
Algebraically
Graphically

3. Solve Algebraically

4. Solve Algebraically 4−𝑥 +15>21

5. Solve on your own: 𝑥+1 −10≤−2
Remember to isolate absolute value
Separate into two equations and reverse.

6. Solution 4−𝑥 +15≥21 −12≤𝑥 𝑎𝑛𝑑 𝑥≤4 −12≤𝑥≤4
−12≤𝑥 𝑎𝑛𝑑 𝑥≤ −12≤𝑥≤4
Why is the format of the solution different?

7. Practice
Pause and solve problems 11, 12, and 13 from lesson 3 in your assignment packet.
11. 2 𝑥− >4
𝑥+1 −4<5
𝑥+4 +2≥5

8. Practice Solutions 11. 𝑥<3 𝑜𝑟 𝑥>4
12. −5<𝑥 𝑎𝑛𝑑 𝑥< −5<𝑥<4
13. 𝑥≤−5 𝑜𝑟 𝑥≥−3
𝑥<3 𝑜𝑟 𝑥>4

9. Solving Graphically 𝑥+3 +1>4
Solve the inequality graphically
Graph both sides of the equation
y= 𝑥+3 +1
𝑦=4

10. Solving Graphically 𝑥+3 +1>4
Solve the inequality graphically
Graph both sides of the equation
y= 𝑥+3 +1
𝑦=4
Intervals on the x axis:
−6≥𝑥 𝑜𝑟 𝑥≥0

11. On your Own Solve: 𝑥 −2 −3≤1
Hint: Begin by graphing both sides

12. On your Own Solve: 𝑥 −2 −3≤1 Final Solution −2≤𝑥≤6
Hint: Begin by graphing both sides
Final Solution
−2≤𝑥≤6
Why different format?

13. Final Thoughts
When does an absolute value inequality apply to a real-world situation?
Remember you can always check your solution but placing a value in for the variable to see if the equation remains true.